Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, 2008. ,
Mixed L 2-Wasserstein Optimal Mapping Between Prescribed Density Functions, Journal of Optimization Theory and Applications, vol.44, issue.2, pp.255-271, 2001. ,
DOI : 10.1023/A:1011926116573
Discretization of functionals involving the Monge???Amp??re operator, Numerische Mathematik, vol.7, issue.5, 2014. ,
DOI : 10.1080/03605308408820337
Numerical resolution of an ???unbalanced??? mass transport problem, ESAIM: Mathematical Modelling and Numerical Analysis, vol.37, issue.5, pp.851-868, 2003. ,
DOI : 10.1051/m2an:2003058
URL : https://hal.archives-ouvertes.fr/inria-00071800
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numerische Mathematik, vol.84, issue.3, pp.375-393, 2000. ,
DOI : 10.1007/s002110050002
Numerical analysis of a multi-phasic mass transport problem, Contemporary Mathematics, vol.353, pp.1-18, 2004. ,
DOI : 10.1090/conm/353/06428
Augmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations, Journal of Optimization Theory and Applications, vol.111, issue.2, pp.1-26, 2015. ,
DOI : 10.1007/s10957-015-0725-9
Iterative Bregman Projections for Regularized Transportation Problems, SIAM Journal on Scientific Computing, vol.37, issue.2, pp.1111-1138, 2015. ,
DOI : 10.1137/141000439
URL : https://hal.archives-ouvertes.fr/hal-01096124
Monotone and consistent discretization of the Monge-Amp??re operator, Mathematics of Computation, vol.85, issue.302, 2014. ,
DOI : 10.1090/mcom/3080
Numerical solution of the Optimal Transportation problem using the Monge???Amp??re equation, Journal of Computational Physics, vol.260, pp.107-126, 2014. ,
DOI : 10.1016/j.jcp.2013.12.015
A mixed finite element method for nonlinear diffusion equations, Kinetic and Related Models, vol.3, issue.1, pp.59-83, 2010. ,
DOI : 10.3934/krm.2010.3.59
Regularized Regression and Density Estimation based on Optimal Transport, Applied Mathematics Research eXpress ,
DOI : 10.1093/amrx/abs007
An Optimization Problem for Mass Transportation with Congested Dynamics, SIAM Journal on Control and Optimization, vol.48, issue.3, pp.1961-1976, 2009. ,
DOI : 10.1137/07070543X
URL : https://hal.archives-ouvertes.fr/hal-00385145
Entropy-diminishing CVFE scheme for solving anisotropic degenerate diffusion equations In Finite volumes for complex applications. VII. Methods and theoretical aspects, Math. Stat, vol.77, pp.187-196, 2014. ,
On systems of continuity equations with nonlinear diffusion and nonlocal drifts, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01147666
Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations, Duke Mathematical Journal, vol.156, issue.2, pp.229-271, 2011. ,
DOI : 10.1215/00127094-2010-211
Numerical Simulation of Diffusive and Aggregation Phenomena in Nonlinear Continuity Equations by Evolving Diffeomorphisms, SIAM Journal on Scientific Computing, vol.31, issue.6, pp.4305-4329, 2009. ,
DOI : 10.1137/080739574
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates, Rev. Mat. Iberoamericana, vol.19, issue.3, pp.971-1018, 2003. ,
Contractions in the 2-Wasserstein length space and thermalization of granular media, Arch. Ration. Mech. Anal, vol.179, issue.2, pp.217-263, 2006. ,
Measure solutions for nonlocal interaction PDEs with two species, Nonlinearity, vol.26, issue.10, pp.2777-2808, 2013. ,
On the Douglas???Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, vol.29, issue.1, pp.293-318, 1992. ,
DOI : 10.1007/BF01581204
Augmented Lagrangian methods Applications to the numerical solution of boundary value problems, of Studies in Mathematics and its Applications, 1983. ,
A dual algorithm for the solution of nonlinear variational problems via finite element methods, Computers and Mathematics with applications, pp.17-40, 1976. ,
Numerical study of a particle method for gradient flows, 2015. ,
The Variational Formulation of the Fokker--Planck Equation, SIAM Journal on Mathematical Analysis, vol.29, issue.1, pp.1-17, 1998. ,
DOI : 10.1137/S0036141096303359
Approximation of Parabolic Equations Using the Wasserstein Metric, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.4, pp.837-852, 1999. ,
DOI : 10.1051/m2an:1999166
Jeux ?? champ moyen. I ??? Le cas stationnaire, Comptes Rendus Mathematique, vol.343, issue.9, pp.619-625, 2006. ,
DOI : 10.1016/j.crma.2006.09.019
JeuxàJeuxà champ moyen. II. Horizon fini et contrôle optimal, C. R. Math. Acad. Sci. Paris, issue.10, pp.343679-684, 2006. ,
Mean field games, Japanese Journal of Mathematics, vol.4, issue.1, pp.229-260, 2007. ,
DOI : 10.1007/s11537-007-0657-8
URL : https://hal.archives-ouvertes.fr/hal-00667356
Convergence of a variational Lagrangian scheme for a nonlinear drift diffusion equation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.3, pp.697-726, 2014. ,
DOI : 10.1051/m2an/2013126
A MACROSCOPIC CROWD MOTION MODEL OF GRADIENT FLOW TYPE, Mathematical Models and Methods in Applied Sciences, vol.20, issue.10, pp.1787-1821, 2010. ,
DOI : 10.1142/S0218202510004799
URL : https://hal.archives-ouvertes.fr/hal-00418511
A diffusive model for macroscopic crowd motion with density constraints, 2015. ,
Convergence of a fully discrete variational scheme for a thin-film equation, 2015. ,
THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION, Communications in Partial Differential Equations, vol.4, issue.1-2, pp.101-174, 2001. ,
DOI : 10.1007/BF00535689
Optimal Transport with Proximal Splitting, SIAM Journal on Imaging Sciences, vol.7, issue.1, pp.212-238, 2014. ,
DOI : 10.1137/130920058
URL : https://hal.archives-ouvertes.fr/hal-00816211
Entropic wasserstein gradient flows, 2015. ,
Topics in Optimal Transportation, Graduate Studies in Mathematics, vol.58, 2003. ,
DOI : 10.1090/gsm/058
Optimal Transport: Old and New, volume 338 of Grundlehren der mathematischen Wissenschaften, 2009. ,
DOI : 10.1007/978-3-540-71050-9